German patent application DE 100 29 513 A1 discloses a device and a method for increasing the operating time of a particle filter until it becomes necessary to clean non-regenerable particle constituents that are, for example, washed out. In this context, however, the fundamental problem remains that the filter has to be dismantled for the cleaning procedure and then re-installed after the cleaning. This procedure entails quite considerable costs, in addition to which the cleaning procedure calls for maintenance to be carried out in the workshop, thus involving temporary downtimes. In order to keep the costs and downtimes as low as possible, loading with particle constituents at high levels is required and allowed to occur. Here, however, the clogging of the channels causes a relatively high waste gas counterpressure which, among other things, has a detrimental impact on the fuel consumption of the internal combustion engine.